The pyramid of Giza in Egypt is built of stone and was completed in 2560 BC. The length of each side of the square base is 230 meters and the vertical height is 146 meters.

1. What volume of stone is needed to form a solid pyramid with these dimensions?

The surface of the pyramid was originally faced with limestone.

2. How many square meters of facing limestone were needed?

1. V = Ab*h/3. Ab = Area of the base.

V = (230)^2 * 146/3 = 2,574,467m^3.

2. Al = P*Hs / 2.

P = 4 * 230 = 920m = Perimeter of the base.

Hs^2 = (b/2)^2 + h^2,
Hs^2 = (230 / 2)^2 + (146)^2 = 34,541
Hs = 186m = Slant Height.

Al = 920 * 186 / 2 = 85,560m^2 = Lateal
area = Amount of limestone needed.

How many square meters of facing limestone were needed?

To find the volume of the pyramid, we can use the formula:

Volume = (1/3) * base area * height

1. To calculate the volume of the pyramid, we need to first find the base area. The base is a square, so the area can be found by squaring the length of one side of the base.

Base Area = (side length)^2

Base Area = 230m * 230m
= 52,900m^2

2. Now we can calculate the volume:

Volume = (1/3) * 52,900m^2 * 146m
= 3,853,333.33m^3

Therefore, the volume of stone needed to form the solid pyramid is approximately 3,853,333.33 cubic meters.

To find the surface area of the pyramid, we can use the formula:

Surface Area = base area + (0.5 * perimeter of base * slant height)

Since the pyramid is facing limestone, we need to find the surface area of each face and sum them up.

The slant height can be found using the Pythagorean theorem:

Slant height = sqrt((side length/2)^2 + height^2)

Slant height = sqrt((230m/2)^2 + 146m^2)
= sqrt(115m^2 + 21316m^2)
= sqrt(21431m^2)
= 146.27m

Now, we can calculate the surface area of one face:

Face Area = (side length * slant height) / 2

Face Area = (230m * 146.27m) / 2
= 16,811.05m^2

Since the pyramid has 4 faces, we can multiply this value by 4 to find the total surface area:

Total Surface Area = 4 * 16,811.05m^2
= 67,244.2m^2

Therefore, approximately 67,244.2 square meters of facing limestone were needed for the pyramid.